The number N() of supermarkets throughout the country that are using a computerized checkout system is described by theinitial-value problemON(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedureover a long period of time.supermarketsBy hand, sketch a solution curve of the given initial-value problem.N5000400030002000100023002000N(1-0.0002N), N(O) - 1.15001000101015230020001500100030004000300020001010(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).N(E)-1515How many supermarkets are expected to adopt the new technology when t= 157 (Round your answer to the nearestinteger)supermarkets

Answered: Image /qna-images/answer/171e951a-26ba-4629-91dd-af45d49fd1a8.jpg

Answered: The number N() of supermarkets…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and po are positive constants, approaches the equilibrium solution p(t) = as t approaches + ∞. 응 dt (a - bp)p; p (to) = Po
Model the following data using an exponential function of the form f(x) = Ab". You need to do this rigorously, that is, set up a system of equations, and solve it to get A and b. Getting the right answer by guessing will earn no credit. (a) f(x) is exponential and goes through the points (1, 2) and (4,6). (b) f(x) is exponential and goes through the points (2, 75) and (5, 9375).
An investor is presented with a choice of two investments: an established clothing store and a new bookstore. Each choice requires the same initial investment and each produces a continuous income stream of 3%, compounded continuously. The rate of flow of income from the clothing store is f(t)=12,000, and the rate of flow of income from the book store is expected to be g(t)=10,000e^0.05t. Compare the future values of these investments to determine which is the better choice over the next 2 years.
Consider the discrete time model for population growth: Na+1 = Ne"(1-N,) with r > 0. (a) Find all steady states. (b) Discuss the stability of each steady state.
Question 3 (a) Consider a model of market equilibrium in which the current supply of firms is a function of the price that is expected to prevail when the product is sold. Assume that the market supply equation is q³(t) = F + Gp and pe is the expected price and F and G are constant parameters of the supply equation. Assume further that suppliers use information about the actual current price and its first and second derivatives with respect to time to form their prediction of the price that will prevail when their product reaches the market. In particular, assume that dp pe=p+b+c- dt d²p dt² tdpd²p=0, then suppliers and b> c> 0. If the current price is constant, so that dt expect the prevailing price to equal the current price. If the current price is rising, so that > 0, then suppliers expect the prevailing price to be higher than the current dt price. How much higher depends on whether the current price is rising at an increasing rate, > 0; or at a decreasing rate, p 0 is a constant…
How am i supposed to solve these tables without the given function? (#5)
(1 point) Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 14 specimens of a particular species, 5 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: to
An ecologist is studying the impacts of air pollution on giant panda populations, specifically on panda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close to the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : i. 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 1 in 3 female baby pandas…

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